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If (a + ib) (c + id) (e + if) (g + ih) =...

If `(a + ib) (c + id) (e + if) (g + ih) = A + iB`, then show that `(a^2 + b^2) (c^2 + d^2) (e^2 +f^2) (g^2+ h^2) = A^2 + B^2`

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Given :
`(a+ib)(c+i d)(e+ i f)(g+ih)=A+iB`
Taking modulus of both sides
`" "|(a+ib)(c+i d)(e+i f)(g+ih)|=|A+ iB|`
`rArr" " |a+ ib||c+i d||e+ i f||g+ih|=|A+iB|`
`rArr" "sqrt( a^(2)+b^(2))*sqrt(c^(2)+d^(2))sqrt(e^(2)+f^(2))sqrt(g^(2)+h^(2)) =sqrt(A^(2)+B^(2))`
Squaring both sides,
`(a^(2)+b^(2))(c^(2)+d^(2)(e^(2)+f^(2))(g^(2)+h^(2))=(A^(2)+B^(2))`
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NAGEEN PRAKASHAN ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATION -MISCELLANEOUS EXERCISE
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